Path Properties of a Generalized Fractional Brownian Motion
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Path Properties of a Generalized Fractional Brownian Motion

  • Author(s): Ichiba, Tomoyuki
  • Pang, Guodong
  • Taqqu, Murad S
  • et al.
Abstract

The generalized fractional Brownian motion is a Gaussian self-similar process whose increments are not necessarily stationary. It appears in applications as the scaling limit of a shot noise process with a power law shape function and non-stationary noises with a power-law variance function. In this paper we study sample path properties of the generalized fractional Brownian motion, including Holder continuity, path differentiability/non-differentiability, and functional and local Law of the Iterated Logarithms.

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